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ullrika at the uncertainty show

Ullrika Sahlin

Senior lecturer

ullrika at the uncertainty show

Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis

Author

  • Ivette Raices Cruz
  • Johan Lindström
  • Matthias C.M. Troffaes
  • Ullrika Sahlin

Summary, in English

Bayesian inference under a set of priors, called robust Bayesian analysis, allows for estimation of parameters within a model and quantification of epistemic uncertainty in quantities of interest by bounded (or imprecise) probability. Iterative importance sampling can be used to estimate bounds on the quantity of interest by optimizing over the set of priors. A method for iterative importance sampling when the robust Bayesian inference relies on Markov chain Monte Carlo (MCMC) sampling is proposed. To accommodate the MCMC sampling in iterative importance sampling, a new expression for the effective sample size of the importance sampling is derived, which accounts for the correlation in the MCMC samples. To illustrate the proposed method for robust Bayesian analysis, iterative importance sampling with MCMC sampling is applied to estimate the lower bound of the overall effect in a previously published meta-analysis with a random effects model. The performance of the method compared to a grid search method and under different degrees of prior-data conflict is also explored.

Department/s

  • Centre for Environmental and Climate Science (CEC)
  • eSSENCE: The e-Science Collaboration
  • MERGE: ModElling the Regional and Global Earth system
  • Mathematical Statistics
  • Computational Science for Health and Environment

Publishing year

2022-12

Language

English

Publication/Series

Computational Statistics and Data Analysis

Volume

176

Document type

Journal article

Publisher

Elsevier

Topic

  • Probability Theory and Statistics

Keywords

  • Bounds on probability
  • Effective sample size
  • Meta-analysis
  • Random effects model
  • Uncertainty quantification

Status

Published

Research group

  • Computational Science for Health and Environment

ISBN/ISSN/Other

  • ISSN: 0167-9473